A good source for aftermarket tyres for your Audi TT RS is Tyres.co.uk. They have choices for your TT RS that include the Michelin Pilot Sport 5 and Continental SportContact 7 in 245/35 ZR19 (93Y) XL. These are the base-line 19-inch factory fitment for 8S generation Audi TT RS. Other aftermarket wheels have varying specifications, so make sure to check the placard, load index, speed rating, and XL before making purchases.
To find the recommended Audi TT RS tyre sizes and cold inflation pressure, look in the driver door at the sticker on the end face. The included documentation for the wheels and tyre replacement also has the information.
Although all four do not have to be replaced at once, since the TT RS is a Quattro model all tyres must match for rolling circumference as well as type, make, and tread pattern. To maintain optimum performance, TT RS tyres should be replaced in axle pairs. If all four tyres cannot be replaced and the other tyres have a wear difference, then all tyres should be replaced. In the United Kingdom it is recommended the new tyres be installed on the rear axle.